Nonlinearity in the Dynamic Properties of Vulcanized Rubber Compounds

1954 ◽  
Vol 27 (1) ◽  
pp. 209-222 ◽  
Author(s):  
W. P. Fletcher ◽  
A. N. Gent
Keyword(s):  
Simple Shear ◽  
Dynamic Modulus ◽  
Dynamic Properties ◽  
Mechanical Vibration ◽  
Frequency Range ◽  
Vulcanized Rubber ◽  
Rubber Compounds ◽  
Chemical Combination ◽  
Wide Range ◽  
Static Shear

Abstract Measurements are described of the dynamic properties of rubber, loaded with various amounts and types of filler, when subjected to mechanical vibration in simple shear at amplitudes from 0 to 3 per cent shear in the frequency range 20 to 120 c.p.s. The decrease of dynamic modulus with increasing amplitude is shown, for a wide range of filler types and concentrations, to be determined by the amount of stiffening produced by the filler. This relationship is not influenced by variations in the vulcanizing ingredients, reasonable variations in state of vulcanization, addition of softener, or imposition of static shear strain. Rubber compounds stiffened by mixture with, or chemical combination of, other polymers exhibit a smaller order of nonlinearity than that described above and also exhibit much lower hysteresis values within the amplitude range 0 to 3 per cent shear.

Dynamic Properties of Rubber. Dependence on Pigment Loading

1941 ◽  
Vol 14 (4) ◽  
pp. 842-857 ◽  
Author(s):  
S. D. Gehman ◽  
D. E. Woodford ◽  
R. B. Stambaugh
Keyword(s):  
Zinc Oxide ◽  
Internal Friction ◽  
Dynamic Modulus ◽  
Dynamic Properties ◽  
Modulus Ratio ◽  
Volume Loading ◽  
Static Modulus ◽  
Black Clay ◽  
At Resonance ◽  
Wide Range

Abstract Dynamic properties are specific for different pigments. Curves show the dependence on pigment loading of the dynamic modulus, ratio of dynamic to static modulus, internal friction, dynamic resilience, and calculated relative heat generation at constant force and at constant amplitude. For the same volume loading, the dynamic modulus and internal friction rank in the order: Superspectra, channel black, zinc oxide, clay, blanc fixe, Thermatomic black, i.e., roughly in the order of particle size. The calculated dynamic resilience depends on the ratio of the modulus to the internal friction and increases in the order Superspectra, channel black, clay, Thermatomic black, blanc fixe, zinc oxide. The dynamic modulus shows an almost linear relation with the internal friction for different loadings of the same pigment. The dynamic modulus is independent of the frequency in the range 20–150 cycles per second. It depends on the amplitude, an effect which may be connected with the warming of the test-piece due to the vibration. The amplitude at resonance for the same driving force is approximately constant at all frequencies for a given rubber compound. The results show the wide range of dynamic properties obtainable with different pigments, and bring out the general principles involved in their use for dynamic purposes.

Effect of Primary Molecular Weight on the Dynamic Properties of Cured Rubber

1959 ◽  
Vol 32 (3) ◽  
pp. 651-661
Author(s):  
E. V. Kuvshinskiĭ ◽  
M. M. Fomicheva
Keyword(s):  
Molecular Weight ◽  
Dynamic Modulus ◽  
Room Temperature ◽  
Dynamic Properties ◽  
Molecular Weights ◽  
Vulcanized Rubber ◽  
Equilibrium Modulus ◽  
Modulus Of Resilience ◽  
Molecular Weight Fractions ◽  
Butadiene Styrene

Abstract 1. Studied were the moduli of resilience and rebound elasticity of the vulcanized rubbers made from fractions of butadiene-styrene rubber “SKS-30-A” at temperatures of 20, 60, and 100° C in the region of molecular weights from 45,000 to 620,000 with various degrees of vulcanization (with variation in the pseudoequilibrium modulus from 5 to 70 kg/cm2). 2. The dynamic modulus of resilience is little dependent on the molecular weight of the original rubber both at room temperature and at higher temperatures. 3. At higher temperatures the elasticity of vulcanized rubber is mainly determined by the degree of vulcanization, the measure of which is the pseudo-equilibrium modulus, and is little dependent on the initial molecular weight. At low temperatures (20° C) elasticity increases with the degree of vulcanization, but it increases at different rates for vulcanized rubbers made from fractions with different molecular weights. At 20° C the increase in the degree of vulcanization increases the elasticity of vulcanized rubbers made from low-molecular fractions (45,000) to a lower degree than of those made from high molecular weight fractions (above 133,000). 4. The value of the maximum elasticity of vulcanized rubbers obtained from rubbers of the same molecular weight is not dependent on the type of accelerator used.

Rubber-Lined Equipment. Fundamental Principles of Design

1937 ◽  
Vol 10 (3) ◽  
pp. 564-573 ◽  
Author(s):  
J. R. Hoover ◽  
H. C. Klein
Keyword(s):  
Hydrochloric Acid ◽  
Physical Properties ◽  
Steel Shell ◽  
Vulcanized Rubber ◽  
Rubber Compounds ◽  
Wide Range ◽  
Steel Tank ◽  
New Material ◽  
Principles Of Design ◽  
Made In

Abstract IN 1924 a process known as Vulca-lock, discovered by chemists of The B. F. Goodrich Company, made possible the first successful steel tank car for hydrochloric acid service. The tank was lined with acid-resisting vulcanized rubber bonded to the steel shell with adhesion exceeding 500 pounds per square inch. A new material of chemical construction was thus made available in practical form. The resulting widespread and rapidly increasing use of rubber-lined equipment in the processing industries is well known. Basically, the value of such construction lies in properly combining the unique corrosion- and abrasion-resistant properties of rubber with the rigidity, strength, and adaptability of steel or other structural materials. It is essential, therefore, that chemical engineers be familiar with certain principles of design, upon which the successful use of rubber-lined equipment depends. No attempt will be made in this paper to define the broad field of usefulness or the limitations of rubber linings. The fact must be emphasized, however, that an extremely wide range of chemical and physical properties is available in commercial rubber compounds and that these compounds, like metals and alloys, are designed for specific uses.

The Dynamic Properties of Carbon Black-Loaded Natural Rubber Vulcanizates. Part I

1963 ◽  
Vol 36 (2) ◽  
pp. 432-443 ◽  
Author(s):  
A. R. Payne
Keyword(s):  
Thermal Treatment ◽  
Carbon Black ◽  
Natural Rubber ◽  
Dynamic Modulus ◽  
Dynamic Properties ◽  
Viscosity Change ◽  
Vulcanized Rubber ◽  
Elastic Responses ◽  
Natural Rubber Vulcanizates

Abstract The dynamic properties of a natural vulcanized rubber containing carbon black were studied for dynamic tensions of amplitude varying greatly. It was shown that both the elastic responses and viscosity change with amplitude of oscillation and with concentration and type of carbon black. The effects of thermal treatment on the dynamic modulus were also studied. Beginning with conditions of equilibrium between the hard and soft regions of the vulcanizate for very weak stresses, the values for the formation of hard regions from soft regions were determined by means of the Van't Hoff isochore.

Measurement of the Dynamic Modulus of Rubber at Very Small Amplitudes with an Optical Interferometer

1960 ◽  
Vol 33 (2) ◽  
pp. 272-274
Author(s):  
N. M. Borovitskaya
Keyword(s):  
Interference Pattern ◽  
Dynamic Modulus ◽  
Dynamic Properties ◽  
Monochromatic Light ◽  
Michelson Interferometer ◽  
Light Modulation ◽  
Wide Range ◽  
Narrow Band Filter ◽  
The Difference ◽  
Set Up

Abstract A method of measuring very small differences of optical path using light modulation by an interferometer has been described. This enables one to measure amplitudes of mechanical vibrations of the order of 0.01 A or even smaller. We have used this method to measure the dynamic modulus of rubber at very small amplitudes. It is desirable to use this method for measuring the dynamic modulus of rubber and other highly elastic substances, firstly because in accuracy and simplicity it has certain advantages over existing acoustic methods. In the second place, it enables one to work at very small amplitudes and, in association with other methods, over a very wide range of amplitudes of deformation. This is of interest in connection with the general theory of the dynamic properties of rubber, and in particular, for checking the linearity of these properties, that is, the independence of the modulus and the loss on the amplitude, in particular for filled rubbers. We will briefly describe the apparatus with which the measurements were made. It consists of a Michelson interferometer and a source of monochromatic light. The interference pattern (lines of equal width) is projected onto the cathode of a photomultiplier. The output of the photo multiplier is fed to the input of a narrow-band filter, to the output of which the measuring instrument is connected. The mirror on the interferometer is set up so that the whole of the interference pattern, or the greater part of it, is uniformly illuminated. If now one of the mirrors vibrates with a frequency ω and an amplitude of z, then the difference in path between the interference beams will vary with a frequency of ω and the intensity of the light falling on the photomultiplier will also change. The current through the photomultiplier will be modulated with a frequency of ω. The first harmonic of the photocurrent will be I1=AJ1(4τz/λ), where λ is the wavelength of light; A is a coefficient depending on the intensity of the interfering beams and on their difference of path with the mirror at rest; I1 is a first order Bessel function.

scholarly journals Very-small to large strain dynamic behaviour of unsaturated sand in a wide range of suction

2020 ◽  
Vol 195 ◽  
pp. 03002
Author(s):  
Ali Akbar Karimezadeh ◽  
Fardin Jafarzadeh ◽  
Anthony Kwan Leung ◽  
Adel Ahmadinezhad
Keyword(s):  
Transition Zone ◽  
Unsaturated Soil ◽  
Simple Shear ◽  
Dynamic Properties ◽  
Large Strain ◽  
Damping Ratio ◽  
Small Strain ◽  
Soil Parameters ◽  
Static And Dynamic Analysis ◽  
Wide Range

Shear modulus (Gmax at very small strain and G at large strain) and constraint modulus at very small strain (M) are important soil parameters for static and dynamic analysis in geotechnical applications. However, these dynamic properties of unsaturated soil are rarely reported. In this study, a cyclic simple shear apparatus was newly-modified for allowing both the shear and constrained moduli at both very small and large strains to be measured. Benders or ultrasonic sensors were embedded in an unsaturated soil sample for transmitting/receiving shear- and pressure-wave, respectively. Two very-small-strain tests were conducted to determine the Gmax, M and soil damping ratio of a sand for a wide range of suction covering from the boundary-effect, transition and residual zone of the water retention curve of the sand. In addition, six large-strain cyclic simple shear tests were carried out to investigate G. The test results showed that Gmax and M were approximately constant before reaching the air-entry value, but there was a significant increase in Gmax as the sand dried further. Yet, M dropped within the transition zone, and interestingly when the suction was beyond the residual value, M increased. M along the wetting path was higher than that along the drying path. The damping ratio, on the other hand, first reduced before reaching the air-entry value, but it increased at the transition zone and then decreased within the residual zone. At large strain, G/Gmax also increased as suction increased until reaching the residual zone, beyond which the normalised value show substantial decreased.

Experimental Study of Low-Frequency Effects on the Dynamic Modulus of a Buna-N Rubber

1955 ◽  
Vol 28 (1) ◽  
pp. 131-138 ◽  
Author(s):  
Allen Q. Hutton ◽  
A. W. Nolle
Keyword(s):  
Dynamic Modulus ◽  
Room Temperature ◽  
Temperature Scale ◽  
Dynamic Properties ◽  
Low Frequency ◽  
Frequency Range ◽  
Frequency Increase ◽  
Frequency Effects ◽  
Similar Compound ◽  
Linear Dynamic

Abstract The linear dynamic Young's modulus of a vulcanized Buna-N gum rubber was measured at frequencies of 0.05, 0.10, and 1.00 cps, in the temperature range − 22° C to 30° C, by a method in which a small differential sinusoidal elongation is superimposed on a 5 per cent static elongation. The width of the dispersion range on the temperature scale (the range in which the logarithm of the modulus increases steeply with decreasing temperature) is only about 10° C, contrasted with widths as great as 25° C found in previous measurements on a similar compound at frequencies of several kilocycles. The modulus-temperature plot shifts upward by only about 4° C per decade of frequency increase of the present range, contrasted with about 10° C per decade in the previous measurements at higher frequencies. It is concluded that this elastomer cannot be described properly by means of the “method of reduced variables”, in which the dynamic properties are ascribed to mechanisms having identical temperature dependence, and that the low-temperature behavior is governed by mechanisms distinct from those effective in the audio-frequency range at room temperature.

scholarly journals Simulation Verification of the Contact Parameter Influence on the Forces’ Course of Cereal Grain Impact against a Stiff Surface

2021 ◽  
Vol 11 (2) ◽  
pp. 466
Author(s):  
Włodzimierz Kęska ◽  
Jacek Marcinkiewicz ◽  
Łukasz Gierz ◽  
Żaneta Staszak ◽  
Jarosław Selech ◽  
...  
Keyword(s):  
Dynamic Properties ◽  
Decisive Role ◽  
Force Sensor ◽  
Contact Forces ◽  
Correct Selection ◽  
Contact Parameter ◽  
Cereal Grain ◽  
Wide Range ◽  
The Impact ◽  
Selection Of

The continuous development of computer technology has made it applicable in many scientific fields, including research into a wide range of processes in agricultural machines. It allows the simulation of very complex physical phenomena, including grain motion. A recently discovered discrete element method (DEM) is used for this purpose. It involves direct integration of equations of grain system motion under the action of various forces, the most important of which are contact forces. The method’s accuracy depends mainly on precisely developed mathematical models of contacts. The creation of such models requires empirical validation, an experiment that investigates the course of contact forces at the moment of the impact of the grains. To achieve this, specialised test stations equipped with force and speed sensors were developed. The correct selection of testing equipment and interpretation of results play a decisive role in this type of research. This paper focuses on the evaluation of the force sensor dynamic properties’ influence on the measurement accuracy of the course of the plant grain impact forces against a stiff surface. The issue was examined using the computer simulation method. A proprietary computer software with the main calculation module and data input procedures, which presents results in a graphic form, was used for calculations. From the simulation, graphs of the contact force and force signal from the sensor were obtained. This helped to clearly indicate the essence of the correct selection of parameters used in the tests of sensors, which should be characterised by high resonance frequency.

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